Does the fact that gravity moves at the speed of light affect how planets move?

[peanutaxis]

TL;DR Summary

Does the fact that gravity moves at the speed of light affect how planets move?

Hi,

If a 1000km space rock called Pluto can meaningfully perturb the orbit of Neptune - which is some 7,800 times more massive - at a distance of no less that 2.4AU, then surely the fact that gravity moves at the speed of light would produce significant effects too(?)

Is there any effect, for instance, from the fact that the earth is attracted to where Mars was 3 minutes ago (at closest distance) and vice versa? (Yes, I realise we also see Mars where is was 3 minutes ago)

Does this have any effect? Is it accounted for when using GR rather than Newton to calculate things?

Thanks in advance.
p

 

[Ibix]

then surely the fact that gravity moves at the speed of light would produce significant effects too(?)

Some care is needed with this statement. It can be quite difficult to define what one means by a "speed of gravity", and when people say it is the speed of light they are generally crossing their fingers behind their back and talking about gravitational waves.

The answer is no, the effect of Mars on Earth's position comes from where it is now, not where it was three minutes ago - with a few important caveats. The maths to explain how this works is very non-trivial, but it is not magic. Effectively the way the maths works predicts the current location based on the past location, and this is where the attraction turns out to point to. But if you could attach large enough rockets to Mars to affect its orbit significantly and suddenly turned them on, you would find that Earth continued to behave as if Mars were in its current orbit until the changes in the gravitational field propagated here. That would happen at or below the speed of light.

 

[PeroK]

TL;DR Summary: Does the fact that gravity moves at the speed of light affect how planets move?

Hi,

If a 1000km space rock called Pluto can meaningfully perturb the orbit of Neptune - which is some 7,800 times more massive - at a distance of no less that 2.4AU, then surely the fact that gravity moves at the speed of light would produce significant effects too(?)

Is there any effect, for instance, from the fact that the earth is attracted to where Mars was 3 minutes ago (at closest distance) and vice versa? (Yes, I realise we also see Mars where is was 3 minutes ago)

Does this have any effect? Is it accounted for when using GR rather than Newton to calculate things?

Thanks in advance.
p

In addition to what @Ibix said, there is no unique definition of "now" or "three minutes ago" in special or general relativity. Simultaneity is relative and depends on the coordinate system you choose.

 

[PeterDonis]

TL;DR Summary: Does the fact that gravity moves at the speed of light affect how planets move?

This classic paper by Carlip is a good treatment of the underlying issue your question is getting at:

https://arxiv.org/abs/gr-qc/9909087

The short version is: in a theory that conserves energy and momentum, where an interaction has a finite speed, to a first approximation we expect the effects of aberration (i.e., the finite speed of the interaction, so a planet is not seeing where the Sun is "now" but only where the Sun was on its past light cone) to be cancelled by velocity-dependent effects that are required in order to conserve energy and momentum.

Once we go to higher orders of approximation, we find that the source-receiver system in isolation (Sun-planet in the case of gravity) does not exactly conserve energy and momentum: some energy and momentum is emitted as radiation. This allows a certain amount of aberration to be observed. How much aberration is observed depends, heuristically, on how easy it is to emit the necessary radiation.

Carlip uses electromagnetism as a test case to illustrate this: aberration effects are fairly easily observable with electromagnetism, and that is because electromagnetic radiation is dipole at lowest order and therefore is "easy" to emit.

By contrast, with gravity, aberration effects are barely observable at all--the cancellation described above is much more exact--because gravitational radiation is quadrupole at lowest order and is therefore much "harder" to emit. But there are small effects such as perihelion precession that show that the cancellation is not quite exact and some gravitational radiation is emitted.

 

[PeterDonis]

the effect of Mars on Earth's position comes from where it is now

No, this is not correct. The effect of the Sun or any other planet on Earth's motion comes from where the Sun or the other planet was on Earth's past light cone. But the effect is not just a Newtonian distance-dependent force; there are also velocity-dependent effects that cancel out most of the aberration effect. See the Carlip paper I referenced in post #4.

 

[PeterDonis]

there is no unique definition of "now" or "three minutes ago" in special or general relativity. Simultaneity is relative and depends on the coordinate system you choose.

Yes, and this is why any correct relativistic theory of the interaction must have the interaction depend only on where the source was on the receiver's past light cone, since that is an invariant and does not depend on any choice of coordinates.

 

[Ibix]

The effect of the Sun or any other planet on Earth's motion comes from where the Sun or the other planet was on Earth's past light cone. But the effect is not just a Newtonian distance-dependent force; there are also velocity-dependent effects that cancel out most of the aberration effect.

Yes - that's what I was getting at when I said "[e]ffectively the way the maths works predicts the current location based on the past location, and this is where the attraction turns out to point to." The aberration effect you refer to is exactly the OP's naive assumption that relativistic gravity would look something like a Newtonian force pointing to where Mars was but, as you and Carlip point out, the velocity dependent terms make it look more like one pointing to where Mars is now. Not realising that there were velocity dependent terms is how Carlip says his reference 1, van Flandern, was mislead into thinking that relativistic gravity must propagate much faster than $c$. Of course the theory cannot gave an effect depend on anything outside the past lightcone - but as far as I understand it Carlip's paper is an explanation of why it (naively and approximately) looks like it can.

 

[DaveE]

But there are small effects such as perihelion precession that show that the cancellation is not quite exact and some gravitational radiation is emitted.

Is this the cause of the precession of Mercury observation that confirmed GR?

 

[PeterDonis]

Is this the cause of the precession of Mercury observation that confirmed GR?

If you break things down the way Carlip does in the paper, yes: perihelion precession is caused by the velocity-dependent components of the interaction.

Carlip's way of breaking down the interaction is not the only way to do so, though. Other ways of doing it can result in attributing perihelion precession to different "causes". These different methods are not really in contradiction to each other; they are just different ways of describing the overall GR solution in reasonably "intuitive" terms.

 

[Hornbein]

TL;DR Summary: Does the fact that gravity moves at the speed of light affect how planets move?

Hi,

If a 1000km space rock called Pluto can meaningfully perturb the orbit of Neptune - which is some 7,800 times more massive - at a distance of no less that 2.4AU, then surely the fact that gravity moves at the speed of light would produce significant effects too(?)

Is there any effect, for instance, from the fact that the earth is attracted to where Mars was 3 minutes ago (at closest distance) and vice versa? (Yes, I realise we also see Mars where is was 3 minutes ago)

Does this have any effect? Is it accounted for when using GR rather than Newton to calculate things?

Thanks in advance.
p

Newton's solution assumes gravity takes effect instantly. It doesn't, but by a remarkable near-cancellation the result is usually quite close. I've long imagined how disappointed Albert would have been if the cancellation were exact.